We say that (REF ) is equivalent to (REF ) because it can be shown [1]} that the optimal solution \(\lbrace {\mathbf {w}}^*, {\mathbf {u}}^*, {\mathbf {v}}^*\rbrace \)  of the former and that of the latter \({\mathbf {p}}^*\)  are related as \(\sqrt{{\mathbf {p}}^*} = {\mathbf {v}}^*\) , where the square root is applied elementwise.
Hence, if we obtain a optimal solution to the (non-convex) problem in (REF ), this would immediately translate into a optimal solution to our problem of interest (REF ). Additionally, the structure in (REF ) is amenable to a block-coordinate descent solution, since the objective is convex in each of the three variables when the other two are fixed.
Indeed, there exist closed-form expressions for these coordinate descent steps.
Our unfolding architecture is inspired by these iteratively applied closed-form solutions, which we augment with learnable parameters.
